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Concepts Of Physics MCQ Edition [Volume 2]PhysicsBohr's Model and Physics of the Atom

An atom (or ion) has a ground state energy of -54.4 eV . This species could be

Options

  1. Adeuterium
  2. BLi ⁺⁺
  3. Chydrogen
  4. DHe ^+

Correct answer

D. He ^+

Step-by-step solution

The energy of an electron in the n^ th orbit of a hydrogen-like species is given by E_n = -13.6 Z^2 n^2 eV . For the ground state, n = 1 . E₁ = -13.6 Z^2 eV Given E₁ = -54.4 eV . -13.6 Z^2 = -54.4 Z^2 = 54.4 13.6 = 4 Z = 2 The species with atomic number Z = 2 is helium. Since the Bohr model applies to single-electron species, the ion is He ^+ .

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